Math Chapter Wise

EnglishPGT 2013

Q101.The maximum area of equilateral triangle inscribe in circle of radius r -

Ar2 B2/r C2 4 r D2 8 r

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EnglishPGT 2010

Q102.For the curve y = xex, the point

Ax = –1 is a point of minimum Bx= 0 is a point of minimum Cx = –1 is a point of maximum Dx = 0 is a point of maximum

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EnglishPGT 2010

Q103.The curve u = x5 – 5x4 + 5x3 –1 on the origin will be

Amaximum Bminimum Cneither maximum nor minimum DNone of the above

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EnglishPGT 2009

Q104.One maximum point of sinp x cosq x is

A1 tan− = p x q Bx = tan–1 q p C1 tan− = p x q D1 tan− = q x p

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EnglishPGT 2009

Q105.Value of tan 1 x x x + is maximum when

Ax = cos x Bx = sec x Cx = cot x DNone of these

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EnglishPGT 2005

Q106.The maximum points on the curve x=ex y is:

A(1, e) B(1,e–1) C(e, 1) D(e–1, 1)

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EnglishPGT 2005

Q107.Water runs into a conical tank at the rate of 9metre3 /sec. The tank stands point down and has height of 10 metres and base radius of 5 metres. How fast will be water level rise when the water is 6 metres deep?

Aπ metres/ sec B1/π metres /sec C2π metres/sec D2/π metres /sec

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EnglishPGT 2005

Q108.A rectangle is to be drawn inside a semicircle of radius 2 cm. What is the largest area of the rectangle it can have?

A5cm2 B4cm2 C3.6cm2 D3.2cm2

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EnglishPGT 2005

Q109.The normal to the curve x2 – xy + y2 = 7 at the point (–1,2) is

A5y=4x+14 B4y=5x+3 C5y+4x=14 D4y+5x=3

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EnglishPGT 2004

Q110.The minimum value of 2 | 3 1| x x − + − + is

A-4 B0 C-3 DNone of the above

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EnglishPGT 2004

Q111.If f(x) = x5 - 20x3 + 240x, then f(x) is

Amonotonically, decreasing everywhere Bmonotonically, decreasing only in (0,∞) Cmonotonically, increasing everywhere Dmonotonically, increasing only in(0,∞)

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EnglishPGT 2004

Q112.The slope of the tangent to the curve y= 4 3 0 1 + + ∫ x dt t dt the point where x = 1, is

A2 B1 C0 D1/4

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EnglishPGT 2004

Q113.The length of the subnormal of the rectangular hyperbola x2 - y2 = a2 at the point (, 2) a a is

A2/a B/ 2/a C2a Da

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EnglishPGT 2003

Q114.The function 250 2 f (x) = x x + + has as minimum value at

Ax = 2 Bx=3 Cx=4 Dx=5

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EnglishPGT 2003

Q115.Find the maximum and minimum value of the function 2 7 6 f (x) = 10 x x x − + −

A0.1 B1, 25 C1, 20 DNone of these

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EnglishPGT 2003

Q116.In case of Rolle’s Theorem which of the following statement is false?

A= f BImage/formula option B (see source) Cf DNone of these

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EnglishPGT 2002

Q117.If (((()))) 1 2 2 3 f(x) 3 x x = − = − then the maximum and minimum values of f(x) are respectively:

A+1and –1 B1 and 1 2 C2 and 0 D0 and –2

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EnglishPGT 2002

Q118.Greatest Value of (1/x)x is:

Ae B() 1 e Ce 1 e DNone of these

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EnglishPGT 2002

Q119.Two positive numbers whose sum is 16 and sum of whose cubes in maximum are given by:

A8, 8 Bno such numbers exist C0, 16 DNone of these

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EnglishPGT 2002

Q120.The minimum value of (((()))) 2 2 2x 2x 1 sin x e − + is:

Ae B1/e C1 D0

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